On several numerical strategies to solve Richards' equation in heterogeneous media with Finite Volumes

Sabrina Bassetto (1, 2) , Clément Cancès (2) , Guillaume Enchéry (1) , Quang Huy Tran (1)

1 IFPEN - IFP Energies nouvelles
2 RAPSODI - Reliable numerical approximations of dissipative systems

We benchmark several numerical approaches building on upstream mobility two-point flux approximation finite volumes to solve Richards' equation in domains made of several rocktypes. Our study encompasses four different different schemes corresponding to different ways to approximate the nonlinear transmission condition systems arising at the interface between different rocks, as well as different resolution strategies based on Newton's method with variable switch. The different methods are compared on filling and drainage test cases with standard nonlinearities of Brooks-Corey and van Genuchten type, as well as with challenging steep nonlinearities.

Mots clés: Richards' equation; heterogeneous domains; finite volumes; Newton's method; parametrization based variable switch

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Sabrina Bassetto, Clément Cancès, Guillaume Enchéry, Quang Huy Tran. On several numerical strategies to solve Richards' equation in heterogeneous media with Finite Volumes. Computational Geosciences, 2022, 26, pp.1297-1322. ⟨10.1007/s10596-022-10150-w⟩. ⟨hal-03259026⟩